Advanced Signal Processing Techniques

High-Frequency Enveloping, Modulation, and Their Role in Vibration Analysis: High-frequency enveloping and modulation are advanced techniques in vibration analysis used to detect and diagnose faults in machinery, particularly in rolling element bearings, gears, and similar components. These methods help identify subtle fault signatures that might be masked by other vibration signals. 1. High-Frequency Vibration Analysis: High-frequency vibrations occur in the ultrasonic range, typically above the audible frequency range (>20 kHz). These signals are often generated by: Rolling element bearings under load. Impacts from pitting, spalling, or cracking. Gear tooth defects. High-frequency analysis involves capturing these ultrasonic vibrations and interpreting them to diagnose faults. 2. Enveloping Technique: Enveloping is a signal processing technique used to extract fault-related signatures from high-frequency vibration signals. It works by isolating the modulation pattern caused by impacts or irregularities in the system. How Enveloping Works: --Demodulation --Filtering --Rectification --Envelope Detection --Frequency Spectrum Analysis The envelope is subjected to Fast Fourier Transform (FFT) to identify characteristic fault frequencies, such as: Ball Pass Frequency Outer Race (BPFO) Ball Pass Frequency Inner Race (BPFI) Ball Spin Frequency (BSF) Fundamental Train Frequency (FTF) 3. Modulation in Vibration Analysis: Modulation refers to the alteration of a carrier signal's amplitude, frequency, or phase due to an underlying fault. In the context of vibration analysis: Faults like bearing defects, gear tooth wear, or misalignment create periodic impacts or variations in force, which modulate the vibration signal. Amplitude Modulation (AM) and Frequency Modulation (FM) are common in machinery diagnostics. 4. Applications of Enveloping and Modulation Analysis --Bearing Fault Diagnosis: Identifying characteristic frequencies like BPFO, BPFI, BSF, and FTF. Gearbox Analysis: Diagnosing gear tooth wear, cracks, or broken teeth. Isolating gear mesh frequencies and their harmonics, modulated by defects. Detection of Lubrication Issues: High-frequency enveloping can reveal lubrication starvation or contamination in rolling element bearings. Rotating Machinery Faults: Detecting misalignment, imbalance, or looseness, especially when these faults cause modulated vibration patterns.

The growing integration of renewable energy into microgrids has raised concerns about islanding, an unplanned state where distributed generation (DG) continues to power a local grid despite losing connection to the main utility. This poses significant safety risks to personnel and operational hazards to the grid, as unsynchronized reconnection can cause substantial equipment damage due to large inrush currents. Therefore, developing highly accurate, fast, and cost-effective IDS (Islanding Detection Systems) for microgrids is crucial. The IDS is critical for solar PV installations as to: • Ensure safety by preventing energized islands during maintenance. • Protect equipment from damage due to unsynchronized operation. • Maintain grid stability and comply with engineering standards as IEEE-1547, which mandate rapid disconnection (e.g., within 2 seconds) if an island forms. IDS methods are categorized as local, remote, and signal processing. The local method is further classified as passive and active. Local active methods (e.g., AFD) offer fast and accurate detection but can degrade power quality, while local passive methods (e.g., O/U F&V) avoid this but have a large Non-Detection Zone (NDZ). Remote methods (e.g., PLC) provide fast detection and a small NDZ, but are expensive and complex. Signal processing methods, such as Fourier-/Wavelet-Transform (FT/WT), and Empirical Mode Decomposition (EMD), aim to reduce the NDZ, but can suffer from aliasing. Their effectiveness in supervised learning prediction accuracy may degrade. To address the drawbacks of active and passive methods, a hybrid Intelligent IDS called 'AVMD-TEO-MPE-1D-CNN' is proposed by the authors of [1]. It's based on a parameter-optimized multiscale variational mode decomposition (VMD) and a deep learning hybrid approach. First, the proposed Adaptive-VMD (AVMD) strategy improves the selection of the optimal mode number and penalty term in VMD by leveraging the relative MPE (multi-scale permutation entropy) between the original signal and the IMFs (intrinsic mode functions). Subsequently, the TEO (Teager Energy Operator) is used to further extract sequential features to track the instantaneous energy of the IMFs. Finally, the AVMD-TEO-MPE-based features in the intelligent IDS are used to train a 1D-CNN (one-dimensional convolutional neural network) as a deep learning binary classifier to distinguish between islanding and non-islanding states. The proposed 'AVMD-TEO-MPE-1D-CNN' method demonstrates 100% accuracy in simulation results for distinguishing islanding from non-islanding events across various conditions, with a maximum detection time of 46.402 ms. It also exhibits noise resistance and outperforms existing methods in comparative analyses. The link to paper [1] is shared in the comments. They developed their simulation using #Matlab, #Simulink, and #Simscape. However, one can use VMD, MPE, and 1D-CNN, available in Python, from various GitHub repository APIs.

My primary passion for the last six years, which is AI/ML, and my primary passion for the first two decades of my career, which was digital signal processing (DSP), have finally found a common point of intersection in the form of Fourier Analysis Networks (FAN). I have discussed in the past (I wrote a post on Komogorov-Arnold Network or KAN about six months ago) that as the input functions increase in complexity, the "universal approximation" foundation of multi-layer neural networks start hitting their limits. Result is too many hidden layers and somewhat unwieldy models. The Komogorov-Arnold Network, based on the Komogorov Representation, is a different approach, that can represent any continuous multi-variate function as a summation of multiple continuous univariate functions. This was quite a breakthrough, and it will continue to serve this field well. One aspect that is so far neglected, which is actually one of the primary objectives in DSP, is to discover, and utilize, the periodicity of data. One of the key benefits is that if there is a periodicity, a time domain input can be represented in a more compact way in the frequency domain. To do this, we use Fourier Analysis, which decomposes a signal into a sum of sinusoidal components, which are fundamental to understanding the periodicity and frequency components of the input. A Fourier Analysis Network (FAN) is a type of neural network that uses the principles of Fourier analysis to model, analyze, and process signals or data. The FANs incorporate sinusoidal functions into their architecture to capture periodic or frequency-domain features of data. Such networks can encode data in the frequency domain, which is particularly useful in scenarios where periodicity is present (such as audio signals and image textures). There are many types of FANs! Here are a few examples. The Fourier Neural Operator (FNO) uses the Fourier Transform to learn mappings between functional spaces, and it is very useful n solving partial differential equations. The Fourier Feature Networks use Fourier feature embeddings to transform input data into a high-dimensional space using sinusoidal functions, and Neural Radiance Fields (NeRF) is a useful application. Finally, Spectral Neural Networks operate entirely in the frequency domain instead of time or spatial domain, and can be used for image compression, denoising and other applications. We like to learn new things in our area of work all the time. But if a "ghost from the past" becomes useful in a new and different way, somehow that becomes even more interesting!

Real-Time Peak Detection System on FPGA | DRDO Internship As part of my DRDO internship, I designed and implemented an adaptive peak detection algorithm for real-time signal analysis on FPGA. The goal was to detect transient peaks in noisy signals with minimal latency and high reliability. 🧠 Algorithm Overview: The system maintains a sliding window of recent signal samples. It continuously calculates the mean and standard deviation over this window to adapt to signal baseline shifts. A new sample is compared against a dynamic threshold, defined as a multiple of the standard deviation above the mean. When the signal exceeds this threshold, it is marked as part of a peak region. A finite state machine (FSM) tracks entry into and exit from peak regions, using a hysteresis margin to ensure stable detection and avoid false triggers. Upon exit from a peak region, the system registers a valid peak along with its location, amplitude, and width. 🛠️ The design is optimized for FPGA implementation with fixed-point arithmetic, ensuring resource efficiency and real-time operation. It is suitable for applications like: Anomaly detection in sensor signals Vibration/event monitoring Embedded signal analytics This was a great opportunity to apply statistical signal processing in hardware and optimize it for defense-grade embedded systems. #FPGA #SignalProcessing #Verilog #PeakDetection #RealTimeSystems #AdaptiveThreshold #HardwareDesign #DRDO #DigitalSignalProcessing #VLSI

Everyone in the EE and signal processing field has heard of the Fourier transform and hopefully the ubiquitous Fast Fourier Transform (FFT). One of the cornerstones of signal processing we know today. You may have even dealt with the Hilbert transform - which is useful when dealing with complex-valued signals leveraged in digital comms, adaptive beamforming, phase/freq estimation, demodulation, channelization, etc, etc. These signals take on many different names in literature: I/Q, quadrature phase, analytic, etc. - where the basis is derived from the Hilbert transform. But have you heard of the Fast Hilbert Transform (FHT)? Probably not. It is something I discovered years back when developing an efficient digital down-converter (DDC) scheme. The serendipitous and incredible outcome is that you can compute the Hilbert transform of a signal without any multiplies or adds. Basically just sign changes. It is the most efficient way to compute a Hilbert transform I have seen, and the encompassing DDC architecture is the most efficient topology to convert a real-valued signal into an analytic (complex-valued) signal I have come across in my experience. You get a 2-4x speedup in compute efficiency over the current state of the art. I discovered this topology while researching ways to improve throughput on a low power multi-channel RF board. If interested I am finishing up a white paper outlining all of this, seeing as I havent made this very well publicized in the past. If you are working on high speed signal processing in FPGAs or processors, or are an ADC chip architect - this might be of worth to you. I can easily envision this filtering structure used in new ADCs designs (that also have onboard digital down conversion blocks) to further reduce power draw in those types of chips while not sacrificing performance. In any event, it was a real eye opener to me in terms of innovating in DSP, when you thought there was nothing new left to figure out or discover. There is still hope to uncover new things...

🚀 Been revisiting one of the most elegant blueprints in signal intelligence: Don H. Johnson’s Statistical Signal Processing (Rice University). It’s not just about filters and noise—it’s about treating uncertainty as a first-class citizen. Whether you’re estimating parameters buried under stochastic chaos 🌪️, or trying to decide between hypotheses in a fog of Gaussian noise 📡, this book is a masterclass in precision 🎯. What really struck me: 🧠 Estimation is an art—you choose the error metric (MSE, absolute error, MAP, ML...) and optimize accordingly. 🔬 Detection is science—if you define optimality correctly (say via likelihood ratios or mutual information), there's often one best answer. ⚠️ And buried in all of this is a quiet warning from Kolmogorov about misusing the Central Limit Theorem. (Hint: tails lie.) There’s something powerful about connecting probability 📈, Hilbert spaces 📐, and real-time inference ⏱️ all under one roof. And it’s a great reminder: before we dive into the latest transformers 🤖 or RAG stacks 🧠, there’s deep wisdom in how we model randomness itself. 💡 If you're working on inference under uncertainty—radar, finance, comms, or even modern AI systems—give this a read. The math won’t lie to you. I'm creating a lot of scientific content which is available on many of media platforms 👇 👇👇 Substack: https://lnkd.in/dTjrF6AP (English) Spotify: https://lnkd.in/dgumrSMR (English) https://lnkd.in/d-gMtCrE (Hebrew) Youtube: https://lnkd.in/dPGJr7WM (English) https://lnkd.in/dydSqeky (Hebrew) Telegram: https://lnkd.in/d_YxVMAR (English) https://lnkd.in/dVVqhNw5 (Hebrew) #SignalProcessing #EstimationTheory #DetectionTheory #MathInAI